In trading, equity can mean several different things. However it usually comes down to the ownership of an asset without any debt involved.
When engaging in leveraged margin trading, your equity is the total value of your open positions minus the total amount of debt used to open those positions.
Equity can also refer to an asset class, or the shares of companies that together add up to its total ownership (also known as stocks). Share traders can be known as equity traders, and the buying of shares in a company can be known as taking part of its equity.